It really depends, but ultimately a lot of social interactions can only happen between two people at once. Say you and your wife get into a fight. Instead of fighting it out & making up. She now has the option to stop fighting you and go hang out with your co-husband - and you aren’t invited. She also has the option to emotionally strong arm you to get her way by not only stonewalling you/withholding affection, but also by threatening to push you out of your marriage for another guy who literally lives with you both.

You’d need to have a lot of trust in your wife - she’d need to have a tremendous amount of emotional stability and be non-manipulative. She’d suddenly have a lot more power in the relationship in a very inequitable way.

My wife and I are very into monogamy. But she has a serious temper and can be very manipulative when she’s angry (she’s gotten better about this, but it’s a known issue). It’d be very easy for her to do something hurtful. I’m not talking about sex, just the emotional threat of turning to someone else for relief from me - and the implied threat of pushing me out.